Question

Express the following to the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$.
$0.\overline{001}$.

Answer 1

$x=0.001$

$x=0.001001001$

$100x=.100100100...$

$100000x=100.100100$

$99900x=100$

$x=\frac{100}{99900}$

$x=\frac{11}{999}$